Heat conduction in a semi-infinite solid subject to time-dependent boundary conditions

M. Aslam Chaudhry; Syed M. Zubair

Heat conduction in a semi-infinite solid subject to time-dependent boundary conditions

M. Aslam Chaudhry^*, Syed M. Zubair

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

3 Scopus citations

Abstract

A closed-form model for the computation of the transient temperature and heat flux distribution in the case of a semi-infinite solid of constant properties is investigated. The temperature and heat flux solutions are presented for time-dependent surface temperature of the forms: (i) T₁(0,t) = T₀(t/t)^ν-1, (ii) T₂(0,t) = T₀ exp(-λt), and (iii) T₃(0,t) = T₀(t/t) exp(-λt), where λ is a real number and ν is a positive real number. The dimensionless (or reduced) temperature and heat flux solutions are presented in terms of the Whittaker function, the generalized representation of an incomplete Gamma function I_α(b, x) which can also be expressed by the complementary error functions. It is also demonstrated that the present analysis covers some well known (classical) solutions as well as a family of new solutions for the heat transfer through a semi-infinite solid.

Original language	English
Title of host publication	Fundamental Problems in Conduction Heat Transfer
Publisher	Publ by ASME
Pages	77-83
Number of pages	7
ISBN (Print)	0791809331
State	Published - 1992

Publication series

Name	American Society of Mechanical Engineers, Heat Transfer Division, (Publication) HTD
Volume	207
ISSN (Print)	0272-5673

ASJC Scopus subject areas

Mechanical Engineering
Fluid Flow and Transfer Processes

Cite this

@inproceedings{6e247d0a05cb42aca0a52aeb007ab7e2,

title = "Heat conduction in a semi-infinite solid subject to time-dependent boundary conditions",

abstract = "A closed-form model for the computation of the transient temperature and heat flux distribution in the case of a semi-infinite solid of constant properties is investigated. The temperature and heat flux solutions are presented for time-dependent surface temperature of the forms: (i) T1(0,t) = T0(t/t)ν-1, (ii) T2(0,t) = T0 exp(-λt), and (iii) T3(0,t) = T0(t/t) exp(-λt), where λ is a real number and ν is a positive real number. The dimensionless (or reduced) temperature and heat flux solutions are presented in terms of the Whittaker function, the generalized representation of an incomplete Gamma function Iα(b, x) which can also be expressed by the complementary error functions. It is also demonstrated that the present analysis covers some well known (classical) solutions as well as a family of new solutions for the heat transfer through a semi-infinite solid.",

author = "Chaudhry, \{M. Aslam\} and Zubair, \{Syed M.\}",

year = "1992",

language = "English",

isbn = "0791809331",

series = "American Society of Mechanical Engineers, Heat Transfer Division, (Publication) HTD",

publisher = "Publ by ASME",

pages = "77--83",

booktitle = "Fundamental Problems in Conduction Heat Transfer",

}

Heat conduction in a semi-infinite solid subject to time-dependent boundary conditions. / Chaudhry, M. Aslam; Zubair, Syed M.
Fundamental Problems in Conduction Heat Transfer. Publ by ASME, 1992. p. 77-83 (American Society of Mechanical Engineers, Heat Transfer Division, (Publication) HTD; Vol. 207).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - Heat conduction in a semi-infinite solid subject to time-dependent boundary conditions

AU - Chaudhry, M. Aslam

AU - Zubair, Syed M.

PY - 1992

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N2 - A closed-form model for the computation of the transient temperature and heat flux distribution in the case of a semi-infinite solid of constant properties is investigated. The temperature and heat flux solutions are presented for time-dependent surface temperature of the forms: (i) T1(0,t) = T0(t/t)ν-1, (ii) T2(0,t) = T0 exp(-λt), and (iii) T3(0,t) = T0(t/t) exp(-λt), where λ is a real number and ν is a positive real number. The dimensionless (or reduced) temperature and heat flux solutions are presented in terms of the Whittaker function, the generalized representation of an incomplete Gamma function Iα(b, x) which can also be expressed by the complementary error functions. It is also demonstrated that the present analysis covers some well known (classical) solutions as well as a family of new solutions for the heat transfer through a semi-infinite solid.

AB - A closed-form model for the computation of the transient temperature and heat flux distribution in the case of a semi-infinite solid of constant properties is investigated. The temperature and heat flux solutions are presented for time-dependent surface temperature of the forms: (i) T1(0,t) = T0(t/t)ν-1, (ii) T2(0,t) = T0 exp(-λt), and (iii) T3(0,t) = T0(t/t) exp(-λt), where λ is a real number and ν is a positive real number. The dimensionless (or reduced) temperature and heat flux solutions are presented in terms of the Whittaker function, the generalized representation of an incomplete Gamma function Iα(b, x) which can also be expressed by the complementary error functions. It is also demonstrated that the present analysis covers some well known (classical) solutions as well as a family of new solutions for the heat transfer through a semi-infinite solid.

UR - https://www.scopus.com/pages/publications/0027060478

M3 - Conference contribution

AN - SCOPUS:0027060478

SN - 0791809331

T3 - American Society of Mechanical Engineers, Heat Transfer Division, (Publication) HTD

SP - 77

EP - 83

BT - Fundamental Problems in Conduction Heat Transfer

PB - Publ by ASME

ER -

Heat conduction in a semi-infinite solid subject to time-dependent boundary conditions

Abstract

Publication series

ASJC Scopus subject areas

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Cite this